A Pierce oscillator is the common term for an oscillator where the transistor amplifier common node is the source for a Metal Oxide Semiconductor Field Effect Transistor (MOSFET) or emitter for a bipolar junction transistor (BJT). In a more general sense, a Pierce oscillator is an oscillator where a transconductance amplifier (high input impedance, high output impedance) serves as the regenerative amplifier with an LC (inductor-capacitor) or crystal resonator in the feedback path.
FIG. 1 is a circuit diagram of a conventional Pierce oscillator amplifier circuit 100, in accordance with the prior art. Pierce oscillator amplifier circuit 100 includes a common source amplifier (M1) 110 with a current mirror load (M2) 120. The common source amplifier 110 can operate in either weak or strong inversion. An external amplitude control loop can be used to adjust the current into the amplifier bias (AmpBias) node 130 to control the transconductance (gm) of M1 110, which will control the amplitude of oscillation. The feedback resistor 140 is used to bias common source amplifier 110.
The conventional circuit of FIG. 1 requires optimization to minimize distortion when used with a specific crystal resonator and load capacitance. If the circuit is required to work over a large range of resonator and load capacitance values, the amplifier must be capable of providing a wide range of transconductance. This requirement can result in amplifiers with a linear operating range that is less than the amplitude of oscillation. Under this condition, the amplifier operates more as a switch and less as a linear gain element.
Under this condition, the current the amplifier can source and sink is not symmetric. The amplifier will achieve the maximum sink current when the voltage at Xin (VXin) is close enough to the positive voltage supply to turn off M1 110. Thus the amplifier output sink current (Isink) is determined by the amplifier bias current (Iamp) and the mirror ratio between M4 150 and M2 120, and is shown in Equation 1.
                              I                      sink            MAX                          =                              -                                                            (                                      W                    /                    L                                    )                                M2                                                              (                                      W                    /                    L                                    )                                M4                                              ⁢                      I            amp                                              (        1        )            The amplifier will achieve its maximum source current when the voltage at Xin reaches its minimum value. The current through M1 110 minus the current through M2 120 is the total current the amplifier can source. Assuming M1 110 remains in saturation, the maximum current the amplifier can source (neglecting output resistance and second order effects) is shown in Equation 2.
                              I                      source            MAX                          =                                            1              2                        ⁢                          μ              n                        ⁢                                                            C                  ox                                ⁡                                  (                                      W                    L                                    )                                            MI                        ⁢                                          (                                                      (                                                                  V                        DD                                            -                                              V                        Xin                                                              )                                    -                                      V                    THP                                                  )                            2                                -                                                                      (                                      W                    /                    L                                    )                                M2                                                              (                                      W                    /                    L                                    )                                M4                                      ⁢                          I              amp                                                          (        2        )            where VDD is the positive supply voltage. In order to achieve large gm values for use with large load capacitance values, large crystal resonator motional resistances and minimize the bias current, (W/L)M1 is usually a relatively large number.
FIG. 2A is graphical diagram of an exemplary waveform 200 from a conventional Pierce oscillator amplifier circuit with asymmetrical output current, in accordance with the prior art. FIG. 2A shows a Positive Metal Oxide Semiconductor (PMOS) amplifier with asymmetrical output current 210. The amount of current that M1 100 can source is much larger than the current M2 120 can sink for a sinusoid input at Xin centered about VTHP of M1 110. At steady state, the amplifier must sink as much current as it sources. This means that M1 110 will be on just long enough to balance the current that flows through M2 120 while M1 110 is off. If M1 110 is on for a fraction of the cycle, the maximum excursion at Xin and Xout below the voltage at which M1 110 turns on will be small. For example, M1 110 will turn on when the input voltage at Xin is less than VDD−VTHP (a PMOSFET threshold below the positive power supply voltage). Since the oscillations start from this point, the oscillations grow asymmetrically such that the maximum amplitude is close to the positive supply voltage. This makes it difficult to measure the oscillation amplitude by measuring the difference between the minimum excursion and the direct current (DC) bias point of oscillation waveform.
The sample response shown in FIG. 2A was measured on a crystal oscillator using the Pierce oscillator amplifier circuit 100 shown in FIG. 1. The output current 210 peaks during the negative half of the cycle because Xin voltage is at its maximum near VDD. This output asymmetry provides enough distortion to activate unwanted third overtone modes of oscillation in crystals. FIG. 2B is graphical diagram 250 of an exemplary amplifier output current versus input voltage of a Pierce oscillator amplifier in accordance with the prior art, wherein M1 110 of FIG. 1 is a PMOS device. As shown in FIG. 2B, the output current is asymmetric with regard to the amplifier DC bias point.
The ratio between the minimum required gm (transconductance) to sustain oscillation at the smallest load capacitance and the maximum required gm to start oscillations at the largest load capacitance can be as much as 1:1000 for voltage controlled crystal oscillator (VCXO) applications. This range cannot be achieved by adjusting the bias current only, so amplifier non-linearities play a role in determining the effective negative resistance the amplifier applies to the crystal. During startup the amplitude of oscillation is small so that the gain of the amplifier is equal to the small signal gain of M1 110. As the amplitude of oscillation approaches its steady state value, the current limiting of M2 120 acts to reduce the large signal equivalent transconductance of the amplifier, which compensates the losses in the crystal resonator. At steady state, the large signal amplifier transconductance exactly compensates any loses in the crystal resonator (and its parasitic elements).
The amplifier nonlinear current limiting is part of the normal operation of the Pierce oscillator amplifier circuit, but Pierce oscillator amplifier circuit 100 of FIG. 1 has asymmetrical current limiting.
FIG. 2A shows that the amount of current that M1 110 can source is larger than the current M2 120 can sink over for a sinusoid input at Xin centered about VTHP of M1 110. At steady state, the amplifier must sink as much current as it sources. This means that M1 110 will be on just long enough to balance the current that flows through M2 120 while M1 110 is off. If M1 110 is on a fraction of the cycle, the minimum excursion at Xin and Xout will be very close to VDD−VTHP since this is the voltage at which M1 110 will turn on. At steady state, the large signal amplifier transconductance exactly compensates any loses in the crystal resonator (and its parasitic elements). This can present an unwanted constraint if the amplifier is used in an amplitude control loop.